Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 6.9 Simple and Compound Interest to secure good marks & knowledge in the exams.
McGraw-Hill Math Grade 8 Answer Key Lesson 6.9 Simple and Compound Interest
Exercises Calculate
Question 1.
How much interest would you earn if you put $500 in a bank for 15 years and received simple interest of 8%?
Answer:
$ 600.00,
Explanation:
Simple Interest SI = \(\frac{P X R X T}{100}\),
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
Amount = Principle + Simple Interest,
SI = Amount – Principle,
P= $500,
R = 8%,
T = 15 yrs,
Simple Interest SI = \(\frac{P X R X T}{100}\),
= \(\frac{500 X 8 X 15}{100}\),
= 5 X 8 X 15,
= 600.
Question 2.
Calculate the simple interest on a bank account where you deposit $500 and earn 12% a year for 5 years.
Answer:
$300.00,
Explanation:
Simple Interest SI = \(\frac{P X R X T}{100}\),
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
Amount = Principle + Simple Interest,
SI = Amount – Principle,
P= $500,
R = 12%,
T = 5 yrs,
Simple Interest SI = \(\frac{P X R X T}{100}\),
= \(\frac{500 X 12 X 5}{100}\),
= 5 X 12 X 5,
= 300.
Question 3.
Calculate the ending balance of your savings account if you deposit $400 and earn simple interest of 7% for 5 years.
Answer:
$540.0,
Explanation:
Simple Interest SI = \(\frac{P X R X T}{100}\),
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years)
Amount = Principle + Simple Interest,
SI = Amount – Principle,
P= $400,
R = 7%,
T = 5 yrs,
Simple Interest SI = \(\frac{P X R X T}{100}\),
= \(\frac{400 X 7 X 5}{100}\),
= 4 X 7 X 5,
= 140
the ending balance = Principle + Interest,
A = 400 + 140 = 540.
Question 4.
Calculate the ending balance of your savings account if you deposited $1,000 and earned simple interest of 6% for 6 years.
Answer:
$1,360.00,
Explanation:
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
Amount = Principle + Simple Interest,
SI = Amount – Principle,
P= $1,000,
R = 6%,
T = 6 yrs,
Simple Interest SI = \(\frac{P X T X R}{100}\),
= \(\frac{1000 X 6 X 6}{100}\),
= 10 X 6 X 6,
= 360, The ending balance = Principle + Interest
A = $1,000 + $360 = $1,360.
Exercises Calculate
Question 5.
Calculate the interest earned over a 5-year period when you deposit $2,000 and earn compound interest of 8% per year.
Answer:
$938.66
Explanation:
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ]
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
P= $1,000,
R = 8%,
n = 5 yrs,
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
CI = 2000 [ 1 + \(\frac{8}{100}\)]5 – 1 ],
=2000 \(\frac{108}{100}\)5Â – 1 ],
= 2000 X 0.469,
= $938.66.
Question 6.
How much interest would you earn if you put $500 in a bank for 20 years and received a compound interest rate of 4%?
Answer:
$595.56,
Explanation:
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
P= $500,
R = 4%,
n = 20 yrs,
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
CI = 500 [ 1 + \(\frac{4}{100}\)]20 – 1 ],
=500 \(\frac{108}{100}\)5Â – 1 ],
= 500 [ 2.19 – 1],
= 500 x 1.19,
= $595.56.
Question 7.
How much money would you owe if you borrowed $2,000 for 5 years, with a compound interest rate of 28%, and did not make any payments during that period?
Answer:
$6871.95,
Explanation:
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
P = Principle Amount,
R =Â Rate of interest in %,
T = Time (Number of years),
P= $2,000,
R = 28%,
n = 5 yrs,
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
CI = 2000 [ 1 + \(\frac{28}{100}\)]5 – 1 ],
=2000 \(\frac{128}{100}\)5Â – 1 ],
= 2000 X 3.435,
= $6871.95.
Question 8.
Is it better to receive compounded interest for 7 years at 12% on your balance of $500, or to receive the same rate of simple interest for 9 years on that same balance?
Answer:
7 years at 12%, Balance, Compound interest $1105.34
Simple interest $140.00,
Explanation:
Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ],
P= $500, R = 12%, n = 7 yrs, Compound Interest CI = P [ 1 + \(\frac{R}{100}\) ]n – 1 ], CI = 500 [ 1 + \(\frac{12}{100}\)]7 – 1 ],
= 500 \(\frac{112}{100}\)7Â – 1 ] = 500[2.210 – 1] = 500 x 1.210,
= $605.34. The ending balance = Principle + Compound interest,
A = $500 + $605.34 = $1,105.34,
Amount = Principle + Simple Interest,
SI = Amount – Principle, P= $500, R = 12%,
T = 9 yrs,
Simple Interest SI = \(\frac{P X R X T}{100}\),
= \(\frac{500 X 12 X 9}{100}\) = 5 x 12 x 9 = 540.00,
The ending balance = Principle + Simple Interest,
A = $500 + $540 = $1,040.00.